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Utility companies warned yesterday that it could take up to a week before power is restored to more than 500,000 residents in Massachusetts who remained without electricity in one of the largest outages in state history.

Tropical Storm Irene damaged more than 20 major transmission lines and caused the largest power outage in Massachusetts since an April 1997 snowstorm that knocked out service for 800,000 customers statewide.

Even as the state’s biggest utilities, NStar and National Grid, dispatched crews to fix power lines, officials asked consumers to be patient. Not only was there extensive damage, they said, but there were also fewer repair crews dispatched from nearby states because they were dealing with the effects of Irene in their own areas.

“We understand it’s very frustrating for everyone, but it is a time-consuming process,’’ said Caroline Allen, a spokeswoman for NStar, which had 200,000 customers without power yesterday afternoon.

Allen said that restoring power can involve clearing trees, replacing cables, fixing transformers, and coordinating with repair crews from phone and cable companies that share utility poles. NStar brought in 45 extra crews from outside Massachusetts yesterday, each one consisting of one or two employees, but it will take days to repair the power lines, Allen said.

Another factor that delays the arrival of repair trucks at customers’ homes: The utility companies have to prioritize their work, first fixing lines that pose a danger to public safety and that feed power into hospitals, police, and fire stations. Then they focus on the main transmission lines that serve the largest numbers of customers.

“After that, we have to go house to house, restoring single lines to single homes,’’ Allen said. “That takes a tremendous amount of time.’’

Without electricity, some Massachusetts residents turned to social media and their smartphones for news updates and to vent their frustrations.

Timothy Regan and his family, who live in Plymouth, lost power at 10 a.m. on Sunday. He said he called NStar, but did not have any luck reaching someone. Before the family’s power was restored yesterday afternoon, he used his smartphone to access the electric company’s website for updates and posted updates on Twitter about his problems with the power company.

“I think that is what people are most angered over, the lack of communication,’’ Regan said.

Allen responded with a request for patience. “The sheer number of outages is staggering,’’ she said. “We’re doing the best that we can, but we’re also asking our customers’ understanding.’’

Deborah Drew, a spokeswoman for National Grid, said 325,000 of its customers in Massachusetts were without power yesterday, and repairs were expected to extend into the weekend.

“This was a widespread storm that left quite a bit of damage,’’ Drew said. “Trees are down, utility poles are snapped.’’

The power outages also affected numerous businesses. For example, six of Wal-Mart’s 47 Massachusetts stores were closed yesterday because of storm-related outages.

National Grid has 3,500 employees working to restore power; the utility has also brought in hundreds of extra workers from states that were unaffected by the storm.

Scott MacLeod, a spokesman for the Massachusetts Emergency Management Agency, attributed the repair delays to the major transmission lines that were disrupted by the storm.

“You can think of those lines as state highways,’’ he said. “Until you get those back on, you’re not going to get to the local roads, so to speak.’’

Although Governor Deval Patrick praised the general response to the storm and urged residents to be patient at a news conference yesterday, Secretary of State William F. Galvin said he was concerned that some residents were not getting clear information about when they would get their power back.

He said companies are responsible for telling customers what the problems are and the estimated time needed to fix them.

Galvin referred to a state law passed in 2009 that requires companies to submit emergency plans that include, among other things, provisions for a communications system, and tougher fines for violations.

“The question is, ‘How do they deal with the plan? Are they prepared?’ ’’ Galvin asked. “In this instance, knowledge is important,’’ so residents can decide whether they can wait out the outage or need to find temporary quarters.

The 2009 law, passed after the Massachusetts utility Unitil took as long as two weeks to restore power after an ice storm the previous winter, gives the Department of Public Utilities the power to hold hearings and levy fines if it determines the response by the utilities has been inadequate.

Yesterday, the state’s secretary of energy and environmental affairs, Richard K. Sullivan Jr., who oversees the Department of Public Utilities, said: “So far, I think the response has been good, but I think the next 24 hours will be crucial. I’m monitoring the response very closely.’’

Smaller utilities elsewhere in the state were less affected by the storm and were having more success reconnecting customers. Alec O’Meara, a spokesman for Unitil Corp., which serves northern Worcester County, said that restoration was “going well, but going slow.’’

Unitil had 2,700 customers without power Sunday night. By yesterday afternoon, that number was down to 750.

Western Massachusetts Electric was down to 1,400 customers without power yesterday, concentrated in Franklin and Berkshire counties, said spokeswoman Sandra Ahearn. On Sunday night, 8,401 of the utility’s customers had lost power.

In Duxbury, Joe Healy, his wife, Sheri Healy, and 11-year-old daughter were without power since 1 p.m. Sunday, after winds toppled several trees in the front yard and blocked the driveway.

“You would hear the trees going down by the lake, snapping. It makes a distinct sound,’’ Healy said as he and a friend used a chainsaw to cut trees yesterday. “At least they didn’t land on my truck.’’

Rick Collins and his wife, Rachel Collins, lost power in their Abington home at 11 a.m. Sunday. Their biggest worry: how to care for their 4-month-old son.

The couple had half their freezer full with baby milk.

They kept the refrigerator door closed as much as possible, and after 29 hours the power was restored.

“We had so much milk stored up in the freezer that we would have thrown out’’ if the outage lasted longer, Collins said.

“I feel bad for those who have to go through a week, especially if they have a little kid.’’

D.C. Denison can be reached at denison@globe.com. Johnny Diaz of the Globe staff contributed to this report.